Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the gyroid wire network

DOI10.1007/s00023-015-0443-8zbMath1351.82127arXiv1208.3266OpenAlexW1533093691WikidataQ114232034 ScholiaQ114232034MaRDI QIDQ295520

Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann

Publication date: 13 June 2016

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3266

zbMATH Keywords

noncommutative geometrylattice systemsdimer systemIsing systemPotts systemquantum wave guides, quantum wiressystems on graphs

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Noncommutative geometry in quantum theory (81R60) Quantum waveguides, quantum wires (82D77)

Related Items (6)

Feynman categories and representation theory ⋮ Local models and global constraints for degeneracies and band crossings ⋮ Twists on the torus equivariant under the 2-dimensional crystallographic point groups ⋮ Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the gyroid ⋮ Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles ⋮ Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid

Cites Work

• Twisted equivariant matter
• The geometry of the double gyroid wire network: quantum and classical
• Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the gyroid
• Galois Cohomology
• Lie groupoids, gerbes, and non-abelian cohomology
• Lecture on topological crystallography
• Quantal phase factors accompanying adiabatic changes
• Standard realizations of crystal lattices via harmonic maps
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